Question

Find the value of c and state the amplitude and period of f (?)

the function f is defined, for all values of x, by `f(x) = 2sin (x/3) + c` , where c is a constant. the graph `y = f(x)` passes through the point `( pi/2 , -3 )`

(a) find the value of c
(b) state the amplitude and period of f
(c) sketch the graph of `f(x)` for `0<= x <= 3pi`

Answer 1

Please see the explanation below

Explanation:

The function is

`f(x)=2sin(x/3)+c`

The graph passes through the point `=(pi/2, -3)`

`-3=2*sin(pi/3*1/2)+c`

`-3=2sin(pi/6)+c`

`sin(pi/6)=1/2`

`c+1=-3`

`c=-4`

The value of `c=-4`

The function is

`f(x)=2sin(x/3)-4`

The amplitude is `=2`

The perod is `T=2pi/(1/3)=6pi`

See the graph below

graph{2sin(x/3)-4 [-2.54, 48.76, -12.15, 13.5]}